Czechoslovakia and carried on by the Czech rep side of things have a strong record in the euro championship. A final (with the one win) or a semi-final every single generation from the 60s to the 00s, until this last generation fecked it up.
The Nedved/Poborsky era that always played very well at Euro's never seemed able to transport that to the World Cup. They were well beaten by Spain and Yugoslavia for 98 qualifying and a loss to Denmark and 3-1 loss to Iceland put them into the playoffs for 2002 where they lost two close games to Belgium. Out in the groups for 2006 despite a great start when Ghana and Italy beat them very comfortably, though the team was getting older by then.
Yes that's a good point about the Czech Republic being better in Euros than World Cups. They outplayed Denmark at Euro 2000 (admittedly it was a dead rubber and both teams were playing for pride, but still neither team wanted to end the tournament without a win), but finished 2nd best to them in the 2002 WC qualifiers. Their performance against the USA at the 2006 World Cup was stunning (probably the best performance y any team in the opening round of group games), before they were clearly outplayed by Ghana in their second game (Cech was their best player and prevented a heavier defeat).
While they did finish 4th in 2006 (although the quarter-final against England was a poor match with barely any attacking quality from either team), I've generally thought that Portugal have looked much better in Euros than World Cups as well.
There was also a sequence of teams enjoying superb, 'upset' runs at major tournaments, failing to qualify for the next one:
- Denmark won Euro 92, and failed to qualify for the 1994 World Cup (to be fair they only got into Euro 1992 after Yugoslavia were disqualified)
- Sweden finished 3rd at the 1994 World Cup, and failed to qualify for Euro 96
- Czech Republic reach the Euro 96 final, and failed to qualify for the 1998 World Cup
- Croatia finished 3rd at the 1998 World Cup, and failed to qualify for Euro 2000 (although the fact that was the only tournament they missed from 1996-2008 was pretty impressive)
- Turkey finished 3rd at the 2002 World Cup, and failed to qualify for the Euro 2004
- Greece won Euro 2004, and failed to qualify for the 2006 World Cup
I would happily take England winning a European Championship title and then failing to qualify for next World Cup though.